What is the replacement for javax.activation package in java 9?

The JavaBeans Activiation Framework is a standalone technology with its own maintenance JSR in the JCP and its own download. Yes, Java SE 9 has deprecated it and has proposes to remove in a future release along with the modules shared with Java EE but this doesn't impact the standalone version. The standalone version will live on. If you are using Maven then this should work:

<dependency>
  <groupId>com.sun.activation</groupId>
  <artifactId>javax.activation</artifactId>
  <version>1.2.0</version>
</dependency>

and if you are developing a module then you can use requires java.activation.

JavaBeans Activation Framework (JAF) is possibly the alternative you are looking for to the existing package.

This standalone release of JAF uses a Java Platform Module System automatic module name of java.activation, to match the module name used in JDK 9. A future version will include full module metadata.

The standalone APIs are supported in modular form only, via the concept of upgradeable modules. Using them, it's possible to use a version of that module from a later release in any phase, i.e., at compile time, build time, or runtime.

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The currently available version for this is 1.2.0 which can be used like this:

Maven

<dependency>
    <groupId>com.sun.activation</groupId>
    <artifactId>javax.activation</artifactId>
    <version>1.2.0</version>
</dependency>

Gradle

compile 'com.sun.activation:javax.activation:1.2.0'

Ivy

<dependency org="com.sun.activation" name="javax.activation" rev="1.2.0" />